So the biggest salary gap is at the beginning and later everything is up to the skill

If you want fancy jobs like Jane Street then "just" degree from random school may not be enough

People with degrees, especially in stem are small (in compare to all ppl) group of people who are willing to put multi year, intense effort studying non trivial things

So yea, just those traits make them more likely to earn more

Go ahead and give degree to somebody without skills in good paying jobs and see whether that person will be milions ahead too